Determining Percent Increase and Decrease
Chapter 3: Determining Percent Increase and Decrease
To find out, plug all the numbers into the equation for finding the percent increase:
% .
. .
x x x x 42
1 208 95 0 045 208 95 percent increase
original amount
increased amount original amount
= -
= -
= -
Now multiply each side of the equation by the denominator on the right, which is x. Then add xto each side and divide by the coefficient of x. Your math should look like this:
. .
. .
. .
. .
. .
.
x x
x x
x x
x x
x x
x
0 045 208 95 0 045 208 95
1
1 045 208 95 1 045
1 045
1 045 208 95 199 95 .
= -
= -
+ = +
=
=
$ $
Last year’s price for the power washer was $199.95.
Looking into Percent Decrease
Computing percent decreasehas a lot of similarities to computing percent increase — you change percents to decimals, you multiply by the original amount, and then you refer to the original amount. However, sometimes the math is just a bit trickier, because you subtract rather than add (subtraction is a more difficult operation for most folks). And the amount of the decrease often gets obscured (you end up computing with a number that wasn’t in the original problem) when you find the reduced amount directly, without sub- tracting. I explain everything you need to know about computing percent decreases in the following sections.
For many of you, the best method for determining whether you’ve made an error in computation is just common sense. You don’t have to be a mathe- matician to have a feel for the answer. If you’re figuring the percent increase in your salary and you get a 400% increase, you’ll probably realize that this isn’t realistic. (If it isrealistic, then we need to talk.) Basically, you see if the answer resembles what you’ve expected; most of the errors come from using the wrong operation, not in the actual arithmetic (because most people use a calculator, anyway).
Finding new totals with decreases
Percent decreases play a huge role in the world of discount pricing. You see advertisements by merchants announcing that certain items, or even all items, are marked down by a particular percent of the original value of the item. The percent decrease is determined by multiplying the decimal equiva- lent of the percent decrease by the original amount.
When you have amount Aand want to determine a percent decrease of p%, you find the
Percent decrease by multiplying A×0.01p.
New total by subtracting 100% – p% and multiplying A×0.01(100 – p).
Multiplying by 0.01 has the same effect as moving the decimal point two places to the left. (You can see more on changing percents to decimals in Chapter 2.) Tip:For the store that has to determine all the new prices of all the red- tagged items, a nice spreadsheet does the job quickly and accurately. In Chapter 5, you see some suggestions for using a computer spreadsheet.
This example should get you going in the right direction with percent decreases: Say that the after-the-holidays sale at a furniture store features 40% off all red-tagged items. What’s the new price of a $3,515 sofa after the 40% decrease in price?
The amount of the decrease is 40%, which is 0.40 as a decimal. First multiply the original amount by the percentage in decimal form: $3,515 ×0.40 = $1,406.
Then subtract that product from the original amount to get the new price:
$3,515 – $1,406 = $2,109.
Figuring out the percent decrease
Say you purchase several thousand dollars’ worth of office supplies and are given a volume discount on the entire order. Your bill just shows the total before the discount and the net cost after the discount. You can determine the percentage of the discount by using the formula for percent decrease.
To find the percent decrease, you divide the amount of the decrease by the original value. Here’s the formula:
percent decrease
original amount amount of decrease
original amount
original amount reduced amount
=
= -
Using this formula, try out the following example problem.
35
Chapter 3: Determining Percent Increase and Decrease
What’s the percent discount if you paid $1,418.55 for an order whose original cost (before the discount) was $1,470?
To solve, simply plug all the numbers into the formula for percent decrease, like so:
.
. . .
1470 00
1470 00 1418 55 0 035 percent decrease= -
= The decimal 0.035 is equivalent to 3.5%.
Restoring the original price from a decreased price
If you purchase a piece of machinery after getting the frequent customer dis- count of 10%, you may want to determine the original cost for insurance pur- poses. To find out that original cost, you use the formula for determining the percent decrease. You let the original amount be represented by x, and then you solve for xin the equation after replacing the other quantities with their respective values.
For example, suppose you’re such a good customer at Tracy’s Tractors that you’re given a 10% discount on your purchase of a new tractor. You have to pay only $7,688.70. You need to insure the tractor at its replacement cost.
What did the tractor cost before the discount?
Using the percent discount formula, replace the percent with 10% and the dis- counted price with $7,688.70. Let the original price be represented by xand solve for x. Here’s what the new equation will look like:
% .
. .
x x x x
10 7688 70
0 10 7688 70 percent decrease
original amount
original amount reduced amount
= -
= -
= -
Now multiply each side of the equation by x. Then subtract xfrom each side and divide by the coefficient of x. Your math will look like this:
. .
. .
. .
. .
. . ,
x x
x x
x x
x x
x x x
0 10 7688 70 0 10 7688 70
1
0 90 7688 70 0 90
0 90
0 90 7688 70 8 543
= -
= - - = - - = -
-
- =
- -
=
$ $
As you can see, the tractor originally cost $8,543.